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 <!DOCTYPE html><html lang="en"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><meta name="generator" content="rustdoc"><meta name="description" content="This module implements Nova’s evaluation engine using `HyperKZG`, a KZG-based polynomial commitment for multilinear polynomials HyperKZG is based on the transformation from univariate PCS to multilinear PCS in the Gemini paper (section 2.4.2 in `&lt;https://eprint.iacr.org/2022/420.pdf&gt;`). However, there are some key differences: (1) HyperKZG works with multilinear polynomials represented in evaluation form (rather than in coefficient form in Gemini’s transformation). This means that Spartan’s polynomial IOP can use commit to its polynomials as-is without incurring any interpolations or FFTs. (2) HyperKZG is specialized to use KZG as the univariate commitment scheme, so it includes several optimizations (both during the transformation of multilinear-to-univariate claims and within the KZG commitment scheme implementation itself)."><title>arecibo::provider::hyperkzg - Rust</title><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/SourceSerif4-Regular-46f98efaafac5295.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/FiraSans-Regular-018c141bf0843ffd.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/FiraSans-Medium-8f9a781e4970d388.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/SourceCodePro-Regular-562dcc5011b6de7d.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/SourceCodePro-Semibold-d899c5a5c4aeb14a.ttf.woff2"><link rel="stylesheet" href="../../../static.files/normalize-76eba96aa4d2e634.css"><link rel="stylesheet" href="../../../static.files/rustdoc-ac92e1bbe349e143.css"><meta name="rustdoc-vars" data-root-path="../../../" data-static-root-path="../../../static.files/" data-current-crate="arecibo" data-themes="" data-resource-suffix="" data-rustdoc-version="1.76.0 (07dca489a 2024-02-04)" data-channel="1.76.0" data-search-js="search-2b6ce74ff89ae146.js" data-settings-js="settings-4313503d2e1961c2.js" ><script src="../../../static.files/storage-f2adc0d6ca4d09fb.js"></script><script defer src="../sidebar-items.js"></script><script defer src="../../../static.files/main-305769736d49e732.js"></script><noscript><link rel="stylesheet" href="../../../static.files/noscript-feafe1bb7466e4bd.css"></noscript><link rel="alternate icon" type="image/png" href="../../../static.files/favicon-16x16-8b506e7a72182f1c.png"><link rel="alternate icon" type="image/png" href="../../../static.files/favicon-32x32-422f7d1d52889060.png"><link rel="icon" type="image/svg+xml" href="../../../static.files/favicon-2c020d218678b618.svg"></head><body class="rustdoc mod"><!--[if lte IE 11]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="mobile-topbar"><button class="sidebar-menu-toggle">&#9776;</button></nav><nav class="sidebar"><div class="sidebar-crate"><h2><a href="../../../arecibo/index.html">arecibo</a><span class="version">0.2.0</span></h2></div><h2 class="location"><a href="#">Module hyperkzg</a></h2><div class="sidebar-elems"><section><ul class="block"><li><a href="#structs">Structs</a></li></ul></section><h2><a href="../index.html">In arecibo::provider</a></h2></div></nav><div class="sidebar-resizer"></div>
-    <main><div class="width-limiter"><nav class="sub"><form class="search-form"><span></span><div id="sidebar-button" tabindex="-1"><a href="../../../arecibo/all.html" title="show sidebar"></a></div><input class="search-input" name="search" aria-label="Run search in the documentation" autocomplete="off" spellcheck="false" placeholder="Click or press ‘S’ to search, ‘?’ for more options…" type="search"><div id="help-button" tabindex="-1"><a href="../../../help.html" title="help">?</a></div><div id="settings-menu" tabindex="-1"><a href="../../../settings.html" title="settings"><img width="22" height="22" alt="Change settings" src="../../../static.files/wheel-7b819b6101059cd0.svg"></a></div></form></nav><section id="main-content" class="content"><div class="main-heading"><h1>Module <a href="../../index.html">arecibo</a>::<wbr><a href="../index.html">provider</a>::<wbr><a class="mod" href="#">hyperkzg</a><button id="copy-path" title="Copy item path to clipboard"><img src="../../../static.files/clipboard-7571035ce49a181d.svg" width="19" height="18" alt="Copy item path"></button></h1><span class="out-of-band"><a class="src" href="../../../src/arecibo/provider/hyperkzg.rs.html#1-609">source</a> · <button id="toggle-all-docs" title="collapse all docs">[<span>&#x2212;</span>]</button></span></div><details class="toggle top-doc" open><summary class="hideme"><span>Expand description</span></summary><div class="docblock"><p>This module implements Nova’s evaluation engine using <code>HyperKZG</code>, a KZG-based polynomial commitment for multilinear polynomials
+    <main><div class="width-limiter"><nav class="sub"><form class="search-form"><span></span><div id="sidebar-button" tabindex="-1"><a href="../../../arecibo/all.html" title="show sidebar"></a></div><input class="search-input" name="search" aria-label="Run search in the documentation" autocomplete="off" spellcheck="false" placeholder="Click or press ‘S’ to search, ‘?’ for more options…" type="search"><div id="help-button" tabindex="-1"><a href="../../../help.html" title="help">?</a></div><div id="settings-menu" tabindex="-1"><a href="../../../settings.html" title="settings"><img width="22" height="22" alt="Change settings" src="../../../static.files/wheel-7b819b6101059cd0.svg"></a></div></form></nav><section id="main-content" class="content"><div class="main-heading"><h1>Module <a href="../../index.html">arecibo</a>::<wbr><a href="../index.html">provider</a>::<wbr><a class="mod" href="#">hyperkzg</a><button id="copy-path" title="Copy item path to clipboard"><img src="../../../static.files/clipboard-7571035ce49a181d.svg" width="19" height="18" alt="Copy item path"></button></h1><span class="out-of-band"><a class="src" href="../../../src/arecibo/provider/hyperkzg.rs.html#1-610">source</a> · <button id="toggle-all-docs" title="collapse all docs">[<span>&#x2212;</span>]</button></span></div><details class="toggle top-doc" open><summary class="hideme"><span>Expand description</span></summary><div class="docblock"><p>This module implements Nova’s evaluation engine using <code>HyperKZG</code>, a KZG-based polynomial commitment for multilinear polynomials
 HyperKZG is based on the transformation from univariate PCS to multilinear PCS in the Gemini paper (section 2.4.2 in <code>&lt;https://eprint.iacr.org/2022/420.pdf&gt;</code>).
 However, there are some key differences:
 (1) HyperKZG works with multilinear polynomials represented in evaluation form (rather than in coefficient form in Gemini’s transformation).